next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
FThresholds :: isFJumpingExponent

isFJumpingExponent -- Checks whether a given number is an F-jumping number



Returns true if t is an F-jumping number of f, otherwise it returns false. This function only works if the ambient ring of R is -Gorenstein

If the ambient ring of f is a domain, the option AssumeDomain can be set to true in order to speed up the computation. Otherwise AssumeDomain should be set to false.

Let R be the ambient ring of f. If the Gorenstein index of R is known, one should set the option QGorensteinIndex to the Gorenstein index of R. Otherwise the function attempts find the Gorenstein index of R, assuming it is between 1 and MaxCartierIndex. By default, MaxCartierIndex is set to 10.

The option FrobeniusRootStrategy is passed to an internal call of frobeniusRoot. The two valid values of FrobeniusRootStrategy are Substitution and MonomialBasis.

i1 : R = ZZ/5[x,y];
i2 : f =  x^4 + y^3 + x^2*y^2;
i3 : isFJumpingExponent(7/12,f)

o3 = true
i4 : isFJumpingExponent(4/5,f)

o4 = true
i5 : isFJumpingExponent(5/6,f)

o5 = false
i6 : isFJumpingExponent(11/12,f)

o6 = true

See also

Ways to use isFJumpingExponent :